I don't remember where most of the previous discussion took place so I've cross-posted this to all three forums (Iris-Talk, Iris-Photos, and Iris-Species).
There was confusion about the identity of an iris being circulated as Iris perrieri. I had posted pictures of the branching which didn't sound correct for what is usually reported for this species.
I've just been searching for information on perrieri again, (since I've got a few seeds using its pollen) and came across this piece that might help clear up the mystery.
I did a screen capture of the page from Google books review of "A Guide to Species Irises" by the British Iris Society and attached it to this e-mail. Apparently, forms with branching from the base do exist in one small part of perrieri's limited range and because of accessibility issues, these forms are what have been collected and distributed. This has lead to a mis-association of perrieri with aphylla, and also to the the confusing mismatch between recorded description and plants in hand.
I'm not in any way, knowledgable enough to debate this position (although it seems like a reasonable explanation); I'm mostly just relating it for the experts to mull over. ;0)